Tiffany is 4 times as old as Daniel. Twelve years ago, Tiffany was 7 times as old as Daniel. How old is Daniel now?
Answer: We can use the given information to write down two equations that describe the ages of Tiffany and Daniel. Let Tiffany's current age be $t$ and Daniel's current age be $d$ The information in the first sentence can be expressed in the following equation: $t = 4d$ Twelve years ago, Tiffany was $t - 12$ years old, and Daniel was $d - 12$ years old. The information in the second sentence can be expressed in the following equation: $t - 12 = 7(d - 12)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $d$ , it might be easiest to use our first equation for $t$ and substitute it into our second equation. Our first equation is: $t = 4d$ . Substituting this into our second equation, we get: $4d$ $-$ $12 = 7(d - 12)$ which combines the information about $d$ from both of our original equations. Simplifying the right side of this equation, we get: $4 d - 12 = 7 d - 84$ Solving for $d$ , we get: $3 d = 72.$ $d = 24$.